Determining the Waldschmidt constant of a collection of points is difficult in general. The Nagata conjecture [1]} states that for \(s\ge 10\)  very general points in \(\mathbb {P}^2\) , a curve \(C\)  passing through each \(p_i\)  with multiplicity at least \(m_i\)  satisfies
\( \deg C \ge \frac{1}{\sqrt{s}}\sum _{i=1}^s m_i. \) 
